Wellek Testing Statistical Hypotheses of Equivalence and Noninferiority, Second Edition

2. Auflage 2010
ISBN: 978-1-4398-0819-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 431 Seiten

While continuing to focus on methods of testing for two-sided equivalence, Testing Statistical Hypotheses of Equivalence and Noninferiority, Second Edition gives much more attention to noninferiority testing. It covers a spectrum of equivalence testing problems of both types, ranging from a one-sample problem with normally distributed observations of fixed known variance to problems involving several dependent or independent samples and multivariate data. Along with expanding the material on noninferiority problems, this edition includes new chapters on equivalence tests for multivariate data and tests for relevant differences between treatments. A majority of the computer programs offered online are now available not only in SAS or Fortran but also as R scripts or as shared objects that can be called within the R system.

This book provides readers with a rich repertoire of efficient solutions to specific equivalence and noninferiority testing problems frequently encountered in the analysis of real data sets. It first presents general approaches to problems of testing for noninferiority and two-sided equivalence. Each subsequent chapter then focuses on a specific procedure and its practical implementation. The last chapter describes basic theoretical results about tests for relevant differences as well as solutions for some specific settings often arising in practice. Drawing from real-life medical research, the author uses numerous examples throughout to illustrate the methods.

Zielgruppe

Researchers and graduate students in statistics, biostatistics, medical and pharmaceutical research, genetics, psychology, and the social sciences.

Autoren/Hrsg.

Wellek, Stefan

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Introduction

Statistical meaning of the concepts of equivalence and noninferiority
Demonstration of equivalence as a basic problem of applied statistics

Major fields of application of equivalence tests

Role of equivalence/noninferiority studies in current medical research

Formulation of hypotheses

Choosing the main distributional parameter

Numerical specification of the limits of equivalence

General Techniques for Dealing with Noninferiority Problems

Standard solution in the case of location parameter families

Methods of constructing exact optimal tests for settings beyond the location-shift model

Large-sample solutions for problems inaccessible for exact constructions
Objective Bayesian methods

Improved nonrandomized tests for discrete distributions

Relationship between tests for noninferiority and two-sided equivalence tests

Halving alpha?

General Approaches to the Construction of Tests for Equivalence in the Strict Sense
The principle of confidence interval inclusion

Bayesian tests for two-sided equivalence

The classical approach to deriving optimal parametric tests for equivalence hypotheses
Construction of asymptotic tests for equivalence

Equivalence Tests for Selected One-Parameter Problems
The one-sample problem with normally distributed observations of known variance

Test for equivalence of a hazard rate to some given reference value with exponentially distributed survival times

Testing for equivalence of a single binomial proportion to a fixed reference success probability

Confidence-interval inclusion rules as asymptotically UMP tests for equivalence

Noninferiority analogues of the tests derived in this chapter

Equivalence Tests for Designs with Paired Observations
Sign test for equivalence

Equivalence tests for the McNemar setting
Paired t-test for equivalence

Signed rank test for equivalence

A generalization of the signed rank test for equivalence for noncontinuous data

Equivalence Tests for Two Unrelated Samples
Two-sample t-test for equivalence

Mann–Whitney test for equivalence

Two-sample equivalence tests based on linear rank statistics

A distribution-free two-sample equivalence test allowing for arbitrary patterns of ties

Testing for dispersion equivalence of two Gaussian distributions
Equivalence tests for two binomial samples
Log-rank test for equivalence of two survivor functions

Multisample Tests for Equivalence
The intersection-union principle as a general solution to multisample equivalence problems

F-test for equivalence of k normal distributions

Modified studentized range test for equivalence

Testing for dispersion equivalence of more than two Gaussian distributions

A nonparametric k-sample test for equivalence

Equivalence Tests for Multivariate Data

Equivalence tests for several dependent samples from normal distributions
Multivariate two-sample tests for equivalence

Tests for Establishing Goodness of Fit
Testing for equivalence of a single multinomial distribution with a fully specified reference distribution
Testing for approximate collapsibility of multiway contingency tables

Establishing goodness of fit of linear models for normally distributed data
Testing for approximate compatibility of a genotype distribution with the Hardy–Weinberg condition

The Assessment of Bioequivalence
Introduction

Methods of testing for average bioequivalence
Individual bioequivalence: criteria and testing procedures
Approaches to defining and establishing population bioequivalence
Bioequivalence assessment as a problem of comparing bivariate distributions
Tests for Relevant Differences between Treatments

Introduction

Exploiting the duality between testing for two-sided equivalence and existence of relevant differences
Solutions to some special problems of testing for relevant differences
Appendix A: Basic Theoretical Results
Appendix B: List of Special Computer Programs

Appendix C: Frequently Used Special Symbols and Abbreviations

References

Author Index

Subject Index

Über Autor(innen)

Stefan Wellek is a professor of biostatistics at the University of Heidelberg and head of the Department of Biostatistics at the Central Institute of Mental Health in Mannheim, Germany.